Rearrangement term in the folding model of the nucleon optical potential

Abstract

Based on the mean-field determination of the single-particle energy in nuclear matter that contains naturally a rearrangement term (RT) implied by the Hugenholtz–van Hove theorem, the folding model of the nucleon optical potential (OP) is extended to take into account the RT using the effective, density dependent CDM3Yn interaction. With the exchange part of the nucleon folded OP treated exactly in the Hartree–Fock manner, a compact nonlocal version of the folding model is suggested in the present work to determine explicitly the isospin-dependent, nonlocal central term of the nucleon OP. To solve the optical model (OM) equation with a complex nonlocal OP, the calculable R-matrix method is used to analyse the elastic neutron and proton scattering on 40,48Ca, 90Zr, and 208Pb targets at low energies. The inclusion of the RT into the folding model calculation of the nonlocal nucleon OP was shown to be essential for the overall good OM description of elastic nucleon scattering. To validate the nonlocal version of the folding model, the OM results given by the nonlocal folded nucleon OP are also compared with those given by the global parametrization of the nonlocal OP using the analytical nonlocal form factor suggested by Perey and Buck.

Nuclear Mean-Field Description of Proton Elastic Scattering by \(^{12,13}\)C at Low Energies

“…While an overall renormalization of the imaginary proton folded potential without RT by a factor around 0.7 is needed for a optical model description of elastic proton scattering data at the considered energies, that with RT is lower, about 0.6. Although the impact by the RT of the local folding approach was pointed in the optical model results for elastic nucleon scattering on the medium-mass 40,48 Ca and 90 Zr targets [7], it fails to analyze the differential cross section of elastic scattering on lighter nuclei like 12 C at low energies, one can see the similar scenario for the case without RT. At the forward angles one can see that the folded optical potential performs quite well, with the predicted elastic cross section.…”

“…The CDM3Y6 version of the folding model for the local nucleon optical potential discussed above has been adopted in this work to calculate the nucleon optical potential for the study of the elastic proton scattering on 12 C and 13 C targets. In the previous results [7], the elastic scattering on intermediate-mass and heavy nuclei can be analyzed successfully without renormalization of the strength of the real folded potential. To evaluate the validity of this argument for the case of light nuclei 12,13 C, we remained unchanged N R = 1 and only adjusted slightly the strength of imaginary potentials, while the phenomenological spin-orbit potential was used [11].…”

“…, in which the exchange potential is non-local in coordinate space. Recently, by R-matrix method, the nucleon-nucleus scattering equation was solved directly with the non-local potential [7]. While, using the Wentzel-Kramers-Brillouin (WKB) approximation for the shift of the scattering wave by the spatial exchange of the incident nucleon and that bound in the target, the exchange term becomes localized [16], the proton optical potential depends explicitly on energy via the proton relative momentum k(E, r) which is determined self-consistently from the folded proton-nucleus potential as…”

“…It has been used to describe not only the equation of state (EOS) of asymmetric nuclear matter but also the isovector of nucleon optical potential [5]. Recently, the density dependence of the CDM3Yn interaction was included on the HF level by the rearrangement term (RT) of the nucleon optical potential derived from the Hugenholtz-van Hove (HvH) theorem [6,7]. The addition of the RT into the folding calculation of the nucleon optical potential was shown to be necessary for the overall good optical model description of elastic nucleon scattering at low energies.…”

“…The folding calculation using CDM3Yn interaction focuses mainly on the scattering from zero-spin and zero-isospin target nuclei. Recent studies indicate that the CDM3Yn interaction can describe well proton-nucleus scattering with intermediate-mass and heavy targets (A ≥ 40) and E > 30 MeV [6,7]. As a result, the description of proton-nucleus scattering on light nuclei at low energies (E 20 MeV) using CDM3Yn is the subject of interest.…”